Floods are among the most severe and impacting natural disasters. Their occurrence rate and intensity have been significantly increasing worldwide in the last years due to climate change and urbanization, bringing unprecedented effects on human lives and activities. Hence, providing a prompt response to flooding events is of crucial relevance for humanitarian, social and economic reasons. Satellite remote sensing using synthetic aperture radar (SAR) offers a great deal of support in facing flood events and mitigating their effects on a global scale. As opposed to multi-spectral sensors, SAR offers important advantages, as it enables Earth’s surface imaging regardless of weather and sunlight illumination conditions. In the last decade, the increasing availability of SAR data, even at no cost, thanks to the efforts of international and national space agencies, has been deeply stimulating research activities in every Earth observation field, including flood mapping and monitoring, where advanced processing paradigms, e.g., fuzzy logic, machine learning, data fusion, have been applied, demonstrating their superiority with respect to traditional classification strategies. However, a fair assessment of the performance and reliability of flood mapping techniques is of key importance for an efficient disasters response and, hence, should be addressed carefully and on a quantitative basis trough synthetic quality metrics and high-quality reference data. To this end, the recent development of open SAR datasets specifically covering flood events with related ground-truth reference data can support thorough and objective validation as well as reproducibility of results. Notwithstanding, SAR-based flood monitoring still suffers from severe limitations, especially in vegetated and urban areas, where complex scattering mechanisms can impair an accurate extraction of water regions. All such aspects, including classification methodologies, SAR datasets, validation strategies, challenges and future perspectives for SAR-based flood mapping are described and discussed.